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 A007606 Take 1, skip 2, take 3, etc. (Formerly M3241) 8

%I M3241

%S 1,4,5,6,11,12,13,14,15,22,23,24,25,26,27,28,37,38,39,40,41,42,43,44,

%T 45,56,57,58,59,60,61,62,63,64,65,66,79,80,81,82,83,84,85,86,87,88,89,

%U 90,91,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,137,138

%N Take 1, skip 2, take 3, etc.

%C List the natural numbers: 1, 2, 3, 4, 5, 6, 7, ... . Keep the first number (1), delete the next two numbers (2, 3), keep the next three numbers (4, 5, 6), delete the next four numbers (7, 8, 9, 10) and so on.

%C Sometimes called the Smarandache sequential sieve.

%C a(A000290(n)) = A000384(n). [_Reinhard Zumkeller_, Feb 12 2011]

%C A057211(a(n)) = 1. [_Reinhard Zumkeller_, Dec 30 2011]

%D C. Dumitrescu & V. Seleacu, editors, Some Notions and Questions in Number Theory, Vol. I, Erhus Publ., Glendale, 1994.

%D R. Honsberger, Mathematical Gems III, M.A.A., 1985, p. 177.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%D F. Smarandache, Properties of Numbers, 1972.

%H R. Zumkeller, <a href="/A007606/b007606.txt">Table of n, a(n) for n = 1..10000</a> [From _Reinhard Zumkeller_, May 13 2009]

%H C. Dumitrescu & V. Seleacu, editors, <a href="http://www.gallup.unm.edu/~smarandache/SNAQINT.txt">Some Notions and Questions in Number Theory, Vol. I</a>.

%H <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>

%F a(n) = n + m*(m+1) where m = floor(sqrt(n-1)). - _Klaus Brockhaus_, Mar 26 2004

%F a(n+1) = a(n) + if n=k^2 then 2*k+1 else 1; a(1) = 1. [From _Reinhard Zumkeller_, May 13 2009]

%t Flatten[ Table[i, {j, 1, 17, 2}, {i, j(j - 1)/2 + 1, j(j + 1)/2}]] (from Robert G. Wilson v Mar 11 2004)

%o (PARI) for(n=1,66,m=sqrtint(n-1);print1(n+m*(m+1),","))

%o a007606 n = a007606_list !! (n-1)

%o a007606_list = takeSkip 1 [1..] where

%o takeSkip k xs = take k xs ++ takeSkip (k + 2) (drop (2*k + 1) xs)

%o -- _Reinhard Zumkeller_, Feb 12 2011

%Y Complement of A007607.

%Y Cf. A007950, A007951, A007952, A048859, A004201.

%K nonn,nice,easy

%O 1,2

%A _N. J. A. Sloane_, _Robert G. Wilson v_, Mira Bernstein (mira(AT)math.berkeley.edu)

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Last modified May 22 11:39 EDT 2013. Contains 225528 sequences.